Thread: Age of Mathematician's Daughters

Two MIT math graduates bump into each other. They hadn’t seen each other in over 20 years.
The first grad says to the second: “how have you been?”
Second: “Great! I got married and I have three daughters now”
First: “Really? how old are they?”
Second: “Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..”
First: “Right, ok.. oh wait.. hmmmm.., I still don’t know”
second: “Oh sorry, the oldest one just started to play the piano”
First: “Wonderful! my oldest is the same age!”

Problem: How old are the daughters?

It is not an issue of probabilities. person #1 knows the number on the building. Now this means that there must be some ambiguity even if he knows both the sum and product. We need a sum that can be formed in two ways. 14 is the only such sum (8,3,3) and (6,6,2). Now identifying one as the oldest means that twins for the oldest are impossible. Therefore (8,3,3) is the only possibility.

I am not sure if the solution you have provided is correct.....if thats the question and you have not forgotten any other information...

there are 3 variables (i.e the age of the girls) and two equations : (1). x.y.z = 72;
(2). x+y+z = a (lets say a constant value).

Now, even if we had known a; I don't think we would have had a solution.

If the question had said that two of them were twins....then I guess it would have been a solution like you have mentioned.

why not the possibilities like (9 4 2) , (12 3 2) into account..... can you explain